一类混沌系统同步时间可控的自适应投影同步  

Time-controllable projective synchronization of a class of chaotic systems based on adaptive method

作　　者：王春华[1] 胡燕[1] 余飞[1] 徐浩[1] 

机构地区：[1]湖南大学信息科学与工程学院,长沙410082

出　　处：《物理学报》2013年第11期137-143,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61274020);湖南省高校重点实验室开放基金(批准号:12K011)资助的课题~~

摘　　要：基于自适应的方法,提出了一种同步时间可控的混沌投影同步方法.该方法针对一类不同的混沌系统设计了通用的同步控制器和参数自适应律,使驱动系统的状态变量和响应系统的状态变量按照给定比例矩阵达到同步,同步误差按预设的指数速率收敛.由于比例矩阵和指数速率不为第三方所知,可提高信息的抗破译能力.同时,通过调节相关控制器参数,可在有限时间内达到投影同步,并实现对同步时间的有效控制.数值模拟结果的对比和分析验证了所提方法是有效的和鲁棒的.To solve the problem of indeterminate synchronization time in different chaotic systems, this paper presents a time-controllable synchronization scheme. A general synchronization controller and parameter update laws are proposed to stabilize the error system, thus the drive and response systems could be synchronized up to a given scaling matrix at a pre-specified exponential convergence rate. The synchronization time formula is strictly deduced, which suggests that the speed of synchronization is determined by several parameters, such as exponential rate, initial system value and other parameters brought in by the controller. By adjusting these param- eters, the performance of the synchronization can be effectively improved. In numerical simulation, two nonidentical 3D autonomous chaotic systems are chosen to verify this method. The error system can be rapidly stabilized, and unknown parameters are also identi？ed correctly. Firally, two groups of time-controllable parameters are given to verify the theory, wherein synchronization of both cases can be obtained quickly and each result of the synchronization is consistent with the theoretical calculation. The synchronization scheme is characterized by high safety and efficiency, and has its potential value in secure communication.

关 键 词：混沌 自适应控制 投影同步 时间可控 

分 类 号：O415.5[理学—理论物理]